临界量子场论中的矩阵乘积态和变分方法
Matrix product states and variational methods applied to critical quantum field theory
摘要：
利用矩阵乘积态（MPS）研究了无限空间格点上（1+1）维具有四次相互作用的大质量实标量场论（$ϕ^4$理论）的二阶量子相变.我们引入并应用一个朴素的变分共轭梯度法，基于虚时间的含时变分原理（TDVP），获得近似的基态，使用相关的激发计算粒子和孤子的质量，并获得谱密度。我们还估计了中心荷使用有限纠缠标度。我们的临界参数值与最近的Monte Carlo结果吻合得很好，改进了早期的研究，其中使用了相关的DMRG方法，验证了这些技术非常适合于研究临界场系统。我们也得到了临界指数，同意，如预期的那样，与横向伊辛模型。此外，我们处理的特殊情况下，均匀的产品状态（平均场理论）分开，表明他们可以用来调查非临界量子场论在一定条件下。
英文摘要：
We study the second-order quantum phase-transition of massive real scalar field theory with a quartic interaction ($ϕ^4$ theory) in (1+1) dimensions on an infinite spatial lattice using matrix product states (MPS). We introduce and apply a naive variational conjugate gradient method, based on the time-dependent variational principle (TDVP) for imaginary time, to obtain approximate ground states, using a related ansatz for excitations to calculate the particle and soliton masses and to obtain the spectral density. We also estimate the central charge using finite-entanglement scaling. Our value for the critical parameter agrees well with recent Monte Carlo results, improving on an earlier study which used the related DMRG method, verifying that these techniques are well-suited to studying critical field systems. We also obtain critical exponents that agree, as expected, with those of the transverse Ising model. Additionally, we treat the special case of uniform product states (mean field theory) separately, showing that they may be used to investigate non-critical quantum field theories under certain conditions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
